Minor fixes to documentation
authorsaiam
Mon, 08 Dec 2008 23:49:48 +0000
changeset 333 50ec1ab32d2d
parent 332 78657bf06302
child 334 0cf3f2be51eb
Minor fixes to documentation
doc/kishna.tex
--- a/doc/kishna.tex	Mon Dec 08 23:47:48 2008 +0000
+++ b/doc/kishna.tex	Mon Dec 08 23:49:48 2008 +0000
@@ -1,4 +1,4 @@
-\documentclass[a4papre,12pt]{article}
+\documentclass[a4paper,12pt]{article}
 
 \usepackage[utf8]{inputenc}
 \usepackage[english]{babel}
@@ -163,26 +163,26 @@
 
 The mathematical formulation of the Runge-Kutta method:
 If we have an initial value problem of the form
-\begin{equation}
+\begin{equation*}
 y' = f(t, y), \quad y(t_0) = y_0.
-\end{equation}
+\end{equation*}
 The we can describe the RK4 method for this problem by equations
-\begin{align}
+\begin{align*}
 y_{n+1} &= y_n + \tfrac{1}{6}h\left(k_1 + 2k_2 + 2k_3 + k_4 \right) \\
 t_{n+1} &= t_n + h \\
-\end{align}
+\end{align*}
 where $y_{n+1}$ is the RK4 approximation of $y(t_{n+1})$, and
-\begin{align}
+\begin{align*}
 k_1 &= f(t_n, y_n) \\
 k_2 &= f(t_n + \tfrac{1}{2}h, y_n + \tfrac{1}{2}h k_1) \\
 k_3 &= f(t_n + \tfrac{1}{2}h, y_n + \tfrac{1}{2}h k_2) \\
 k_4 &= f(t_n + h, y_n + h k_3) \\
-\end{align}
+\end{align*}
 The next value $(y_n+1)$ is determined by the present value $(y_n)$,
 the product of the interval $(h)$ and an estimated slope that is
 defined as $\frac{1}{6}h\left(k_1+2k_2+2k_3+k_4\right)$.
 
-something network related?
+% TODO: something network related?
 
 \section{Known bugs}
 A lots of them (or maybe not).